Although this shouldn't really come as a surprise because of the LTE radio squeezed in there, but Verizon's Samsung Galaxy Nexus has been shown to be a bit thicker than the GSM version of the phone. As you can see in the picture above, Verizon's LTE version on the right is 9.47 mm, but the GSM version on the left is 8.94 mm thick. To give you a good comparison & contrast, the Droid Bionic is about 10.16 mm, and the Droid RAZR is 7.1 mm.
Also of note is that the Verizon version will have an 1850mAh battery instead of the 1750mAh on the GSM version, which also makes the Verizon version weigh in about 150 grams more. If you want to see the updated full specs on Google's Nexus page, along with a 360 degree view of the phone, you can check it out here: Google - Galaxy Nexus.